Respuesta :
Answer:
2 and - 2 2/3
Step-by-step explanation:
[tex]2x + {3x}^{2} = 16 \\ {3x}^{2} + 2x - 16 = 0 \\ D= {2}^{2} - 4 \times 3 \times ( - 16) = 4 \times 192 = 196 \\ \sqrt{D} = \sqrt{196} = 14 \\ x = \frac{ - 2 + 14}{3 \times 2} = \frac{12}{6} = 2 \\ x = \frac{ - 2 - 14}{3 \times 2} = \frac{ - 16}{6} = - 2 \times \frac{2}{3} [/tex]
ANSWER:
Twice a number is added to three times it’s square. The number is 2, -2.67
SOLUTION:
Let the number be x.
Given, twice a number is added to three times it’s square.
twice a number + three times it’s square
2 [tex]\times[/tex] number + 3 [tex]\times[/tex] numbers square
[tex]2 \times x+3 \times(x)^{2}[/tex]
[tex]2 x+3 x^{2}[/tex]
Also given that, result is 16. So the above equation is equal to 16
[tex]\begin{array}{l}{2 x+3 x^{2}=16} \\ {3 x^{2}+2 x-16=0}\end{array}[/tex]
Let us find roots of above equation using quadratic formula.
[tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
Here, a = 3, b = 2, c = -16
[tex]\mathrm{x}=\frac{-2 \pm \sqrt{2^{2}-4 \times 3 \times(-16)}}{2 \times 3}[/tex]
On simplification we get,
[tex]\begin{aligned} &=\frac{-2 \pm \sqrt{4+12 \times 16}}{6} \\ &=\frac{-2 \pm \sqrt{196}}{6} \\ &=\frac{-2 \pm 14}{6} \\ &=\frac{-2+14}{6}, \frac{-2-14}{6} \\ &=\frac{12}{6}, \frac{-16}{6} \end{aligned}[/tex]
x = 2, -2.67
Hence, the value of "x" is either 2 or -2.67
